Q: Jane walks 5 km at an angle of $$60^\circ$$ north of east from her starting point. What are the eastward (x) and northward (y) components of her displacement vector $$\vec{d}_J$$?

$$x = 4.33\ \text{km},\ y = 2.5\ \text{km}$$

Q: Sam walks 8 km due east along 12th Street. Jane walks 5 km at $$60^\circ$$ north of east from the same starting point. What is the straight-line distance between their endpoints?

$$\sqrt{(8-2.5)^2$ + (0-4.33)^2$} = 6.5\ \text{km}$$

Q: A right triangle has an adjacent side of 4 m and an opposite side of 3 m. What is the length of the hypotenuse?

$$\sqrt{4^2$ + 3^2$} = 5\ \text{m}$$

Q: A student walks 60 m every minute for 4 minutes, then increases their speed and covers 100 m each minute for the next 5 minutes. What is the average velocity for the entire 9-minute trip?

$$\frac{540\ \text{m}}{9\ \text{min}} = 60\ \text{m/min}$$

Q: A student walks east 0.55 km, then north 3.25 km. What is the straight-line distance from the starting point to the final destination?

$$\sqrt{0.55^2$ + 3.25^2$} = 3.30\ \text{km}$$

Q: A student walks 120 m east, then 160 m north. What is the magnitude of the total displacement?

$$\sqrt{120^2$ + 160^2$} = 200\ \text{m}$$

Question 1

Jane walks 5 km at an angle of $$60^\circ$$ north of east from her starting point. What are the eastward (x) and northward (y) components of her displacement vector $$\vec{d}_J$$?

Accepted Answer

$$x = 4.33\ 	ext{km},\ y = 2.5\ 	ext{km}$$

Question 2

Sam walks 8 km due east along 12th Street. Jane walks 5 km at $$60^\circ$$ north of east from the same starting point. What is the straight-line distance between their endpoints?

Accepted Answer

$$\sqrt{(8-2.5)^2$ + (0-4.33)^2$} = 6.5\ 	ext{km}$$

Question 3

Which of the following best describes how to add two vectors $$\vec{A}$$ and $$\vec{B}$$ graphically?

Accepted Answer

Place the tail of $$\vec{B} at $$the tip of $$\vec{A}$$, then draw the resultant from the tail of $$\vec{A} to $$the tip of $$\vec{B}.$$

Question 4

A right triangle has an adjacent side of 4 m and an opposite side of 3 m. What is the length of the hypotenuse?

Accepted Answer

$$\sqrt{4^2$ + 3^2$} = 5\ 	ext{m}$$

Question 5

A car moves along a straight road. Its position vs. time graph is a straight line with a positive slope. What does this indicate about the car's motion?

Accepted Answer

The car is moving at a constant speed in the positive direction.

Question 6

A student walks 60 m every minute for 4 minutes, then increases their speed and covers 100 m each minute for the next 5 minutes. What is the average velocity for the entire 9-minute trip?

Accepted Answer

$$\frac{540\ 	ext{m}}{9\ 	ext{min}} = 60\ 	ext{m/min}$$

Question 7

Which velocity vector diagram best represents a bicycle moving to the left with increasing speed?

Accepted Answer

All velocity vectors point to the left and increase in length.

Question 8

A car starts at $$x = 10 km$$, moves to $$x = -20 km in 30 $$minutes, stays there for 10 minutes, and returns to $$x = 0 km in 40 $$minutes. What is the total displacement?

Accepted Answer

$$-10 km$$

Question 9

If a position vs. time graph is a horizontal line, what does this indicate about the object's motion?

Accepted Answer

The object is not moving.

Question 10

A student walks east 0.55 km, then north 3.25 km. What is the straight-line distance from the starting point to the final destination?

Accepted Answer

$$\sqrt{0.55^2$ + 3.25^2$} = 3.30\ 	ext{km}$$

Question 11

Which of the following statements about displacement vectors is correct?

Accepted Answer

Displacement vectors show the shortest distance between two points.

Question 12

A car's position vs. time graph shows a line that slopes downward. What does this indicate?

Accepted Answer

The car is moving to the left.

Question 13

If a car's displacement vectors are lengthening over time, what does this indicate about the car's motion?

Accepted Answer

The car is speeding up.

Question 14

A student walks 120 m east, then 160 m north. What is the magnitude of the total displacement?

Accepted Answer

$$\sqrt{120^2$ + 160^2$} = 200\ 	ext{m}$$

Question 15

Which of the following is true about the sum of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

The sum can be smaller than either vector if they point in opposite directions.

Representing Motion and Vectors in Physics

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